How do I calculate the median income of each census tracts in a 0-100 percentile form?

[wolfgangBag]

I have a dataset (please see the attachment), and I was wondering how would I calculate the percentage value of each Median Income per Tract (column 1 of the dataset)? My first thought was to sort the Median Income column, gets its median value, and then compare each Tract's Median Income with the median value of the whole column. This way I would get how much far each Tracts Median Income income is from the median value. But that doesn't sound right in my head and I am probably overthinking something here. Can someone please help me figure it out? Maybe some other column/s from this dataset can be utilized to get the most accurate percentage value of Median Income of each Tract.

I would really appreciate if someone can give me a right formula so I can get the percentages of Median Income. Thank you!

 

[afos]

I'm not sure I am following. By definition, the median corresponds to 50%. Could you please rephrase your question?

 

[wolfgangBag]

Thank you afos for reply. I seriously don't know how else to put it I just needed to change each median income in there percent form.

 

[Dr.Peterson]

I have a dataset (please see the attachment), and I was wondering how would I calculate the percentage value of each Median Income per Tract (column 1 of the dataset)? My first thought was to sort the Median Income column, gets its median value, and then compare each Tract's Median Income with the median value of the whole column. This way I would get how much far each Tracts Median Income income is from the median value. But that doesn't sound right in my head and I am probably overthinking something here. Can someone please help me figure it out? Maybe some other column/s from this dataset can be utilized to get the most accurate percentage value of Median Income of each Tract.

I would really appreciate if someone can give me a right formula so I can get the percentages of Median Income. Thank you!

The trouble is that what you ask for is not clearly defined. Percentages must be percentages of something; percentiles are not quite the same thing, but require a data set that they are relative to. So saying "the percentage value of each median income tract" fails to say, "percentage of what?" Possibly you are asking what percentile each tract falls into, in terms of the entire list. But this would not be related to the median of the whole column. And you would surely know how to find percentiles in a column in Excel, using one of the PERCENTRANK functions.

If you can't think of a different way to express what you want, you might tell us what you plan to do with the results, and why. If this is to fulfill some requirement or request, state that exactly as given to you.

 

[JeffM]

I suspect what is wanted is merely to express the listed median incomes as a percentage of the median for the entire list. That is easy enough to do with a spreadsheet. Compute the median of the list and then divide each listed median by the median of the list using a percentage formatting designation.

However, I am dubious that the resulting percentages are meaningful because the tracts have significantly different populations. Thus, the median of the listed medians is unlikely to represent the median of the population.

Unless we understand what meaning is being looked for, we may unwittingly give very bad advice.

 

[wolfgangBag]

The trouble is that what you ask for is not clearly defined. Percentages must be percentages of something; percentiles are not quite the same thing, but require a data set that they are relative to. So saying "the percentage value of each median income tract" fails to say, "percentage of what?" Possibly you are asking what percentile each tract falls into, in terms of the entire list. But this would not be related to the median of the whole column. And you would surely know how to find percentiles in a column in Excel, using one of the PERCENTRANK functions.

If you can't think of a different way to express what you want, you might tell us what you plan to do with the results, and why. If this is to fulfill some requirement or request, state that exactly as given to you.

Hi Yeah I know of that Excel function. Thank you for clarification. I am working with a teacher who wants something like that polar chart in the attachment. I have told her that previous calculation which were done to find those median percentage values are NOT correct. She wants me to do same thing. That's why I am so baffled by it, and asking everywhere how to get it. Frankly I have never seen them in a percentage form.

Her instruction was she needs them in percentage form so she can compare each tracts in the polar chart. And the dataset was given to me, which is in my question. That's all.

 

[wolfgangBag]

I suspect what is wanted is merely to express the listed median incomes as a percentage of the median for the entire list. That is easy enough to do with a spreadsheet. Compute the median of the list and then divide each listed median by the median of the list using a percentage formatting designation.

However, I am dubious that the resulting percentages are meaningful because the tracts have significantly different populations. Thus, the median of the listed medians is unlikely to represent the median of the population.

Unless we understand what meaning is being looked for, we may unwittingly give very bad advice.

Thank you! That's my worry too that it won't be representative. Plus I am pretty sure Median of Medians is questionable. That's why it sounded weird in my head.

 

[JeffM]

Thank you! That's my worry too that it won't be representative. Plus I am pretty sure Median of Medians is questionable. That's why it sounded weird in my head.

So this is a real learning experience.

Sometimes teachers make errors by accident.

Sometimes teachers do not have a clue what they are talking about.

If your teacher asks you to do something stupid, just do it. and hope your next teacher has a clue. There are two different things involved in going to school: one is getting credentials; the other is actually learning something useful The two are not necessarily co-extensive.

 

[wolfgangBag]

So this is a real learning experience.

Sometimes teachers make errors by accident.

Sometimes teachers do not have a clue what they are talking about.

If your teacher asks you to do something stupid, just do it. and hope your next teacher has a clue. There are two different things involved in going to school: one is getting credentials; the other is actually learning something useful The two are not necessarily co-extensive.

Thank you sir! I will just do it. You're right. I asked her if she wanted me to reach out to a statistics teacher, she said "We are not in mathematics or economics where we need to do everything right way. We just need a scale where we can compare them. Even if the methodology is questionable" But I just don't want to give something wrong and get her and myself ridiculed.
I hope you have seen her plot from previous study, here is in the attachment again, it looks janky and wrong. It's weird feeling to do something wrong. Anyhow, I will do my job regardless maybe I am just overthinking it. Thank you again sir, and please stay safe!

 

[Dr.Peterson]

Hi Yeah I know of that Excel function. Thank you for clarification. I am working with a teacher who wants something like that polar chart in the attachment. I have told her that previous calculation which were done to find those median percentage values are NOT correct. She wants me to do same thing. That's why I am so baffled by it, and asking everywhere how to get it. Frankly I have never seen them in a percentage form.

Her instruction was she needs them in percentage form so she can compare each tracts in the polar chart. And the dataset was given to me, which is in my question. That's all.

First, clearly you didn't mean to ask for a percentile.

Second, it would not be appropriate to give the percent of the total of all median incomes, or of the median of medians.

But for this kind of chart, what you really want is just something proportional to the given data, and pretending to be a percentage value. The goal is merely to compare, so exactly what it is doesn't matter so much.

Each other number in the chart is a percentage, not of something pertaining to the whole, but of that individual population: what percentage of the residents of a cluster are white, or unemployed, or whatever. Median income is not like that; it isn't, say, the percent of people who are rich. But for your purposes it will probably be good enough just to produce a number between 0 and 100 (really 0 and 1) that is proportional to the median income of the cluster.

So I would just divide each median income by the largest of them, so that the richest would score 100%. (If you did this relative to the median of medians, then half the numbers would be greater than 100%, which is illegal on such a chart.) This in effect pretends that the income of the richest is the goal for all: "my neighborhood is 80% rich, yours is only 35% rich".

Since no other category ever reaches 100%, you might want to scale that down; you could just arbitrary halve each percent you get to the highest is 50%, or take it relative to the highest median income of any neighborhood in the country.

In any case, it won't really be the same type of value as the others, but it may be a sufficiently reasonable fake.

 

[wolfgangBag]

First, clearly you didn't mean to ask for a percentile.

Second, it would not be appropriate to give the percent of the total of all median incomes, or of the median of medians.

But for this kind of chart, what you really want is just something proportional to the given data, and pretending to be a percentage value. The goal is merely to compare, so exactly what it is doesn't matter so much.

Each other number in the chart is a percentage, not of something pertaining to the whole, but of that individual population: what percentage of the residents of a cluster are white, or unemployed, or whatever. Median income is not like that; it isn't, say, the percent of people who are rich. But for your purposes it will probably be good enough just to produce a number between 0 and 100 (really 0 and 1) that is proportional to the median income of the cluster.

So I would just divide each median income by the largest of them, so that the richest would score 100%. (If you did this relative to the median of medians, then half the numbers would be greater than 100%, which is illegal on such a chart.) This in effect pretends that the income of the richest is the goal for all: "my neighborhood is 80% rich, yours is only 35% rich".

Since no other category ever reaches 100%, you might want to scale that down; you could just arbitrary halve each percent you get to the highest is 50%, or take it relative to the highest median income of any neighborhood in the country.

In any case, it won't really be the same type of value as the others, but it may be a sufficiently reasonable fake.

Thank you sir! Hahaha, that last sentence made me chuckle. Yeah that's what I was being aksed for. And I am just struck with "But why??" Rather than giving out something wrong and laughable, we should just not report that stats. But she is determined to get it, and I am going to perform what you @JeffM have suggested me. I don't want to get into a bad side. I am just an undergrad. I really appreciate your time for answering my question. Please take care of yourself and stay safe!

 

[JeffM]

Thank you sir! Hahaha, that last sentence made me chuckle. Yeah that's what I was being aksed for. And I am just struck with "But why??" Rather than giving out something wrong and laughable, we should just not report that stats. But she is determined to get it, and I am going to perform what you @JeffM have suggested me. I don't want to get into a bad side. I am just an undergrad. I really appreciate your time for answering my question. Please take care of yourself and stay safe!

And this is exactly why many people do not trust any academic study; such people believe that the answers are always predetermined by ideology.

 

[wolfgangBag]

100% agreed!